The total surface area of cuboid of dimension ` a xx a xx b` is.________.

Answer

To find the total surface area of a cuboid with dimensions \( a \times a \times b \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Dimensions**:
The dimensions of the cuboid are given as \( a \), \( a \), and \( b \). Here, we can denote:
- Length \( L = a \)
- Breadth \( B = a \)
- Height \( H = b \)

2. **Formula for Total Surface Area**:
The formula for the total surface area (TSA) of a cuboid is given by:
\[ \text{TSA} = 2(LB + BH + HL) \]

3. **Substituting the Dimensions**:
Substitute the values of \( L \), \( B \), and \( H \) into the formula:
\[ \text{TSA} = 2(a \cdot a + a \cdot b + b \cdot a) \]

4. **Calculating Each Term**:
- \( LB = a \cdot a = a^2 \)
- \( BH = a \cdot b = ab \)
- \( HL = b \cdot a = ab \)

5. **Combine the Terms**:
Now, substitute these values back into the TSA formula:
\[ \text{TSA} = 2(a^2 + ab + ab) = 2(a^2 + 2ab) \]

6. **Final Expression**:
Factor out the common terms:
\[ \text{TSA} = 2a^2 + 4ab \]
or
\[ \text{TSA} = 2(a^2 + 2ab) \]

### Final Answer:
The total surface area of the cuboid with dimensions \( a \times a \times b \) is:
\[ \text{TSA} = 2(a^2 + 2ab) \]